Question

A block of mass $4kg$ is pressed against the wall by a force of $80N$ as shown in figure. Determine the value of friction force and acceleration of block respectively. (Take coefficient of static friction $0.2$, coefficient of kinetic friction $0.15$)

• A. $8N,0m/s^2$
• B. $32N,6m/s^2$
• C. $8N,6m/s^2$
• D. $32N,2m/s^2$

Answer 1

The correct option is A $8N,0m/s^2$

The FBD of the block is as shown in the figure.

From the FBD,
$N=80\cos {37}^{\circ }=64N$
So, $f_L=\mu N=0.2\times 64=32N$

In vertical direction, as $mg<80\sin {37}^{\circ }$, friction force $f$ will act downwards.

Net applied force in upward direction (excluding friction force) is
$80\sin {37}^{\circ }-40=48-40=8N$
As $F_{applied}$ in vertical direction is less than $f_L$, block will not move in vertical direction and value of static friction force will be, $f=8N$